1 votes 1 votes Find the no. of seven digit integers with sum of digits = 11 and formed by using the digits 1,2 and 3 only ? Combinatory combinatory + – dd asked Sep 2, 2016 retagged Jun 27, 2017 by Arjun dd 700 views answer comment Share Follow See 1 comment See all 1 1 comment reply dd commented Sep 2, 2016 i edited by dd Sep 2, 2016 reply Follow Share here summation is 11, a small number, we can partition 11 into 3 groups. But what about large digit sum ? should we use this partition method or use generating function ? 0 votes 0 votes Please log in or register to add a comment.
Best answer 2 votes 2 votes 7 digit number by 1,2,3 and sum 11 The number will be combination of 2 2 2 2 1 1 1 =$\frac{7!}{4!3!}$=35 or, 3 3 1 1 1 1 1=$\frac{7!}{2!5!}$=21 or, 3 2 2 1 1 1 1=$\frac{7!}{2!4!}$=105 So, total such numbers possible=35+21+105=161 srestha answered Sep 2, 2016 selected Sep 2, 2016 by vijaycs srestha comment Share Follow See all 5 Comments See all 5 5 Comments reply Show 2 previous comments vijaycs commented Sep 2, 2016 reply Follow Share First of all it depends on question and I don't think in gate exam we will be asked such question tough question .. 1 votes 1 votes dd commented Sep 2, 2016 reply Follow Share question is not trying, its about time. take any digit sum like 48 (say) suing 1,2,3,4 0 votes 0 votes Sushant Gokhale commented Sep 4, 2016 reply Follow Share @Debashish. I think you have solved one recurrance like this. The recurrance would go like this: let, P(sum) = #ways/permutations to form the given sum Thus, P(sum) = P(sum - 3) (if 3 is the MSB) + P(sum - 2) (if 2 is the MSB) + P(sum - 1) (if 1 is the MSB) Also, questions in GATE are such that they can be solved in 1 or 2 minute(s) mostly with simple techniques unless tricky :) 0 votes 0 votes Please log in or register to add a comment.